For the item you are asking about, a weighed portion of the food (called an aliquot) is subjected to an extraction by a pure solvent to remove quantitatively the analyte (the acrylamide). A method that can detect the small amounts of the analyte is used to get a signal, and that is compared to a standard of the analyte at a known concentration.
In practice, the method for acrylamide has to be able to separate it from other interfering substances also extracted from the aliquot of food. It usually also needs to see separately at a similar quantity an external standard so a comparison can be made. It also has to be able to see the analyte in parts per million or parts per billion- this is typically a GC-MS or HPLC-MS method...
There are additional methods used to verify the quantitative nature of the extraction and account for matrix effects. These are addition of an internal standard, and method of standards addition. An internal standard is added to the food and allowed to extract along with the analyte. It is assumed that they both behave in the same fashion to being extracted. The method standards addition, adds controlled amounts of the analyte to the food, so that matrix effects on the extraction can be studied over a range of concentrations- these are teased out by plotting the measurements vs the varied concentrations of standard and unknown.